ON THE VARIATION OF ZONAL GRAVITY COEFFICIENTS OF A GIANT PLANET CAUSED BY ITS DEEP ZONAL FLOWS

Abstract

Rapidly rotating giant planets are usually marked by the existence of strong zonal flows at the cloud level. If the zonal flow is sufficiently deep and strong, it can produce hydrostatic-related gravitational anomalies through distortion of the planet’s shape. This paper determines the zonal gravity coefficients, J2n ,n = 1,2,3 ,..., via an analytical method taking into account rotation-induced shape changes by assuming that a planet has an effective uniform density and that the zonal flows arise from deep convection and extend along cylinders parallel to the rotation axis. Two different but related hydrostatic models are considered. When a giant planet is in rigid-body rotation, the exact solution of the problem using oblate spheroidal coordinates is derived, allowing us to compute the value of its zonal gravity coefficients ¯ J2n ,n = 1,2,3 ,... , without making any approximation. When the deep zonal flow is sufficiently strong, we develop a general perturbation theory for estimating the variation of the zonal gravity coefficients, ΔJ2n = J2n − ¯ J2n ,n = 1,2,3 ,... , caused by the effect of the deep zonalflows for an arbitrarily rapidly rotating planet. Applying the general theory to Jupiter, we find that the deep zonal flow could contribute up to 0.3% of the J2 coefficient and 0.7% of J4. It is also found that the shape-driven harmonics at the 10th zonal gravity coefficient become dominant, i.e., ΔJ2n ¯ J2n for n5.